How to make vertices more uniform
Relax (Loop Tools)

Loop tools add-on brings in a nice operator called Relax that is capable of "relaxing" the selection that should works well in your particular situation.



In alternative, without adding any external add-on to your Blender's copy, you can select each circumference and run the To sphere operator (Shift+Alt+S) and type 1 (max value).



You can give a try even to the Smooth Vertex operator, but it give best results if the loop to fix is between two loops that have the right shape.